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Conditional Local Nondeterminism and Hausdorff Measure of Level Sets

Published online by Cambridge University Press:  20 November 2018

Narn-Rueih Shieh
Narn-Rueih Shieh*
Affiliation:
Department of Mathematics, National Taiwan University, Taipei, Taiwan
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Abstract

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Let X be a real stochastic process. We localize S. M. Berman's formulation on the local nondeterminism of X to a fixed level. With this localized idea, we prove that, for large classes of Gaussian and Markov X, at each x the level set X(t, w) = x has infinite Hausdorff ϕ - measure (ϕ is certain measure function) for w in a set of positive probability.

Keywords

60G17.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 1 , 01 March 1991 , pp. 123 - 127
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Berman, S. M., Local nondeterminism and local times of Gaussian processes, Indiana Univ. Math. J. 23 (1973), 69–94.Google Scholar
2. Berman, S. M., Local nondeterminism and local times of general stochastic processes, Ann. Inst. Henri Poincaré XIX(1983), 189–207.Google Scholar
3. Berman, S. M., The modulator of the local time, Comm. on Pure and Applied Math. XLI(1988), 121–132.Google Scholar
4. Fristedt, B. and Pruitt, W., Lower function for increasing random walks and subordinators, Z. Wahrscheinlichkeitstheorie verw. Gebiete 18 (1971), 167–182.Google Scholar
5. Kahane, J. P., Some random series of functions. D. C. Heath, 1968.Google Scholar
6. Marcus, M. B., Capacity of level sets of certain stochastic processes Z. Wahrscheinlichkeitstheorie verw. Gebiete 34 (1976), 279–284.Google Scholar